Abnormal subgrain growth in a dislocation-based model of recovery

Simulation of subgrain growth during recovery is carried out using two-dimensional discrete dislocation dynamics on a hexagonal crystal lattice having three symmetric slip planes. To account for elevated temperature (i) dislocation climb was allowed and (ii) a Langevin type thermal noise was added to the force acting on the dislocations. During the simulation, a random ensemble of dislocations develop into subgrains and power-law type growth kinetics are observed. The growth exponent is found to be independent of the climb mobility, but dependent on the temperature introduced by the thermal noise. The in-depth statistical analysis of the subgrain structure shows that the coarsening is abnormal, i.e. larger cells grow faster than the small ones, while the average misorientation between the adjacent subgrains remains nearly constant. During the coarsening Holt's relation is found not to be fulfilled, such that the average subgrain size is not proportional to the average dislocation spacing. These findings are consistent with recent high precision experiments on recovery.Comment: 17 pages, 11 figure

Dynamic Length Scale and Weakest Link Behavior in Crystal Plasticity

Plastic deformation of heterogeneous solid structures is often characterized by random intermittent local plastic events. On the mesoscale this feature can be represented by a spatially fluctuating local yield threshold. Here we study the validity of such an approach and the ideal choice for the size of the representative volume element for crystal plasticity in terms of a discrete dislocation model. We find that the number of links representing possible sources of plastic activity exhibits anomalous (super-extensive) scaling which tends to extensive scaling (often assumed in weakest-link models) if quenched short-range interactions are introduced. The reason is that the interplay between long-range dislocation interactions and short-range quenched disorder destroys scale-free dynamical correlations leading to event localization with a characteristic length-scale. Several methods are presented to determine the dynamic length-scale that can be generalized to other types of heterogeneous materials

The role of weakest links and system size scaling in multiscale modeling of stochastic plasticity

Plastic deformation of crystalline and amorphous matter often involves intermittent local strain burst events. To understand the physical background of the phenomenon a minimal stochastic mesoscopic model was introduced, where microstructural details are represented by a fluctuating local yielding threshold. In the present paper, we propose a method for determining this yield stress distribution by lower scale discrete dislocation dynamics simulations and using a weakest link argument. The success of scale-linking is demonstrated on the stress-strain curves obtained by the resulting mesoscopic and the discrete dislocation models. As shown by various scaling relations they are statistically equivalent and behave identically in the thermodynamic limit. The proposed technique is expected to be applicable for different microstructures and amorphous materials, too.Comment: 13 pages, 12 figure

Dislocation patterning in a two-dimensional continuum theory of dislocations

Understanding the spontaneous emergence of dislocation patterns during plastic deformation is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were proposed, but few of them (if any) are derived from microscopic considerations through systematic and controlled averaging procedures. In this paper we present a two-dimensional continuum theory that is obtained by systematic averaging of the equations of motion of discrete dislocations. It is shown that in the evolution equations of the dislocation densities diffusionlike terms neglected in earlier considerations play a crucial role in the length scale selection of the dislocation density fluctuations. It is also shown that the formulated continuum theory can be derived from an averaged energy functional using the framework of phase field theories. However, in order to account for the flow stress one has in that case to introduce a nontrivial dislocation mobility function, which proves to be crucial for the instability leading to patterning